Recursive difference filter realization of digital filters

ABSTRACT

According to an aspect of the present disclosure, a method comprises computing first set of coefficients of a digital filter providing first filter performance, computing a second set of coefficients from the first set of coefficients, forming a difference digital filter with second set of coefficients to produce a difference filter output and adding a compensation factor to the difference filter output to achieve a second performance identical to the first filter performance. According to another aspect, the second set of coefficients are computed as difference between the successive first set of coefficients such that when the first set of coefficients comprises N number of coefficients, the second set of coefficients comprises N−1 number of coefficients. The method further comprises computing first set of coefficients according to a first relation, computing the second set of coefficients according to a second relation, generating the difference filter output in accordance with a third relation, computing a compensation factor in accordance with a fourth relation and generating a filtered output samples from a set of input samples in accordance with a fifth relation.

CROSS REFERENCES TO RELATED APPLICATIONS

This application claims priority from Indian patent application No.201741017348 filed on May 17, 2017 which is incorporated herein in itsentirety by reference.

BACKGROUND Technical Field

Embodiments of the present disclosure relate generally to system, methodand apparatus of digital signal processing and in particular to digitalfilter realization with reduced complexity.

Related Art

The digital signal is processed for efficient transmission, reception,rendering and for storing information. The information in analog form isoften digitized for processing in digital domain. Digital filteroperation is one of the signals processing operations performed on theinformation bits to eliminate or remove the unwanted informationcomponent. Digital Filters are often deployed for elimination ofunwanted information in the certain frequency bands or ranges. Forexample, Infinite Impulse response (IIR) filters, Finite ImpulseResponse (FIR) filters and autoregressive-moving-average (ARMA) filtersare often deployed for the purpose. The filters are implemented as partof a digital processor operative to perform the desired operation byexecuting the set of instruction or within an integrated circuit withdedicated circuitry. The implementation is generally process intensiveand/or complex in terms of circuit elements including multipliers,adders and the likes. It is desirable to reduce the complexity ofimplementation of these digital/discrete filters.

SUMMARY

According to an aspect of the present disclosure, a method comprisescomputing first set of coefficients of a digital filter providing firstfilter performance, computing a second set of coefficients from thefirst set of coefficients, forming a difference digital filter withsecond set of coefficients to produce a difference filter output andadding a compensation factor to the difference filter output to achievea second performance identical to the first filter performance.

According to another aspect, the second set of coefficients are computedas difference between the successive first set of coefficients such thatwhen the first set of coefficients comprises N number of coefficients,the second set of coefficients comprises N−1 number of coefficients. Themethod further comprises computing first set of coefficients accordingto a first relation, computing the second set of coefficients accordingto a second relation, generating the difference filter output inaccordance with a third relation, computing a compensation factor inaccordance with a fourth relation and generating a filtered outputsamples from a set of input samples in accordance with a fifth relation.

Several aspects are described below, with reference to diagrams. Itshould be understood that numerous specific details, relationships, andmethods are set forth to provide a full understanding of the presentdisclosure. One who skilled in the relevant art, however, will readilyrecognize that the present disclosure can be practiced without one ormore of the specific details, or with other methods, etc. In otherinstances, well-known structures or operations are not shown in detailto avoid obscuring the features of the present disclosure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram illustrating an example system in whichvarious aspects of the present disclosure may be seen.

FIG. 2A is a conventional feed forward or Finite Impulse Response (FIR)filter.

FIG. 2B is an example frequency response or characteristic of an FIRfilter (also referred interchangeably as performance).

FIG. 3 is a conventional Infinite Impulse Response (IIR) filter (alsoreferred as Autoregressive).

FIG. 4 is a conventional ARMA filter.

FIG. 5 is a block diagram illustrating example implementation of afilter in an embodiment.

FIG. 6 is a block diagram illustrating example implementation of a FIRfilter in an embodiment.

FIG. 7 is a graph illustrating the values of b₀[l] and b₁[l] in anembodiment.

FIG. 8A is an example FIR filter in one embodiment.

FIG. 8B is an example filter in one embodiment.

FIG. 9A is an example outputs of a conventional 200 tap low pass FIRfilter using b₀[l] coefficients quantized to 11 bits.

FIG. 9B is an example output of the FIR filter implemented as per theinvention involving a difference FIR filter using b₁[l] coefficientsrepresented by 6 bits.

FIG. 10 is a block diagram illustrating example implementation of an IIRfilter in an embodiment.

FIG. 11A through 11C are block diagrams illustrating recursivedeployment of the difference filters in one embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EXAMPLES

FIG. 1 is a block diagram illustrating an example system in whichvarious aspects of the present disclosure may be seen. The block diagramis shown comprising data source 110, signal conditioner 120 and datareceiver 130. Each module is further described below.

The data source 110 provides data in digital form for signal processingand conditioning. For example, the data source may be representing areceiver front end circuitry receiving wireless signal through knownprotocol like Wi-Fi, Bluetooth, 4G, GSM, RF, Near Field Communicationfor example. Alternately, the Data source may also represent a circuitryconverting analog signal to digital samples like Analog to DigitalConvertor (ADC) converting voice/audio into sequence of binary digits.

The data receiver 130 receives conditioned or (processed) data bits fromthe signal conditioner 120 for further processing. For example, the datareceiver 130 may comprise a transmitter section to transmit the dataover wireless network, a receiver circuitry to decode the data streamand extract information for example.

The signal conditioner 120 performs signal conditioning operation andprovides the conditioned data on path 123. The conditioned data on path123 enable the data receiver 130 to perform desired operation on thesequence of data from the data source 110. For example, the signalconditioner may perform amplification, filter operation, level shiftingoperation, buffer, impedance matching, down conversion of frequency, upconversion of frequency, for example.

In one embodiment, the signal conditioner 120 performs filter operationssuch as low pass filter, band pass filter, high pass filter for example,to pass a desired frequency signal and stop other frequency signals. Inthat, the filters are designed to perform operation on the sequence ofthe binary digits representing the samples of information and providethe sequence of binary digits with removal of undesired information. Themanner in which the signal conditioner 120 may be implemented with thereduced complexity is further described below by first describingconventional filter operations.

FIG. 2A is a conventional feed forward or Finite Impulse Response (FIR)filter. As shown there the FIR filter comprises delay unit 210A through210N, multiplier 220A through 220L and summing unit 230 together operateas FIR filter to produce sequence of output bits y[n] from the sequenceof input bits x[n] as is well known in the art. For example, the outputsequence y[n] is generated from the input sequence x[n] as per therelation:

$\begin{matrix}{{y\lbrack n\rbrack} = {\sum\limits_{l = 0}^{L}\;{{b\lbrack l\rbrack}{x\left\lbrack {n - l} \right\rbrack}}}} & (1)\end{matrix}$

In that, the term b[/] represents the coefficients of multiplier 220Athrough 220L for l taking value of 0 to L. The Notation Σ represent thesumming unit 230 and the term x[n−l] represents the output from thedelay unit 210A through 210L. As is known in the art, the FIR filter 201is commonly referred to as L Tap FIR filter or (L−1) order FIR filter.Each tap implements a multiplier to multiply coefficient b[l] with thecorresponding delayed input data x[n−l].

FIG. 2B is an example frequency response or characteristic of an FIRfilter (also referred interchangeably as performance). The filtercharacteristic is shown with pass band 240, stop band 250, pass bandripple 260, stop band ripple 270 and transition band 280. The one ormore characteristics may be adjusted, altered or set by selecting thenumber of taps, coefficients of multipliers using one or more knowntechniques.

FIG. 3 is a conventional Infinite Impulse Response (IIR) filter (alsoreferred as Autoregressive). As shown there the IIR filter comprisesdelay unit 310A through 310K, multiplier 320A through 320K and summingunit 350 together operate as IIR filter to produce sequence of outputbits y[n] from the sequence of input bits x[n] as is well known in theart. For example, the output sequence y[n] is generated from the inputsequence x[n] as per the relation:

$\begin{matrix}{{y\lbrack n\rbrack} = {{x\lbrack n\rbrack} - {\sum\limits_{k = 1}^{K}\;{{a\lbrack k\rbrack}{y\left\lbrack {n - k} \right\rbrack}}}}} & (2)\end{matrix}$

In that, the term a[k] represents the coefficients of multiplier 320Athrough 320K for K taking value of 1 to K. The notation Σ represent thesumming unit 350 and the term y[n−k] represents the output from thedelay unit 310A through 310K.

Similarly, FIG. 4 is a conventional ARMA filter. As shown there the ARMAfilter 401 comprises IIR filter 410, FIR filter 420 and summation unit430. The IIR 410 and FIR 420 are implemented similar to the conventionalIIR in FIG. 3 and conventional FIR in FIG. 2A. The output sequence y[n]is generated from the input sequence x[n] as per the relation:

$\begin{matrix}{{y\lbrack n\rbrack} = {{\sum\limits_{l = 0}^{L}\;{{b\lbrack l\rbrack}{x\left\lbrack {n - l} \right\rbrack}}} - {\sum\limits_{k = 1}^{K}\;{{a\lbrack k\rbrack}{y\left\lbrack {n - k} \right\rbrack}}}}} & (3)\end{matrix}$

As may be seen, each filter implementation comprises multiplicationoperation multiplying the tapped [delayed] input sequence with at leastone of the multiplication coefficients b[l] and a[k]. Thus, requiring atleast L or K numbers of multiplication operations. Often implementationof the filters (multipliers) is complex in terms of hardware,computation intensiveness and power consumption. In one prior technique,the complexity of implementation is reduced by choosing fixedcoefficients. In one conventional implementation, canonical signed digit(CSD) representations are used in that, the multiplier is implementedusing shift and add technique. In another conventional technique, thecomplexity is reduced by sharing resources such as multiplier byoverlooking and reusing. In that, one multiplier is reused after onefetch or after read operation from the memory.

FIG. 5 is a block diagram illustrating example implementation of afilter in an embodiment. In block 510, coefficients for each tap of afilter are computed for a desired performance or filter characteristicusing conventional technique. For example, the coefficients b[l] and/ora[k] for L and/or K tap filter providing a desired performance as inrelation (1) through (3).

In block 520, a set of difference coefficients representing differencebetween the adjacent coefficients (adjacent taps) are computed. Forexample, the difference coefficients may be computed by finding thedifference between the b[0] and b[1], b[1] and b[2] so on.

In block 530, implementing a difference filter using the differencecoefficients to generate a difference filter output y₁[n]. For example,the difference coefficients are multiplied with the corresponding tapped(delayed) input sequence and added to form a difference filter output.

In block 540, a compensation factor is computed for obtaining thedesired filter characteristic of relation (1) through (3).

In block 550, a filter output is generated by adding difference filteroutput y₁[n] to the compensation factor. In one embodiment the filteroutput y[n] is generated by relation: y[n]=y₁[n]+CF[n]. In that, CF[n]represent compensation factor.

Due to computation of the difference between the conventionalcoefficients, the difference coefficients, may be represented with fewernumber of bits as against the a[k] or b[l], thereby reducing thecomplexity of multiplication in terms of computational power or hardwarerequirement while maintaining the performance of the filter on par withconventional filter of K or L tap with a[k] or b[l] coefficients. Themanner in which each discrete filter may be implemented in exampleembodiments is further described below.

FIG. 6 is a block diagram illustrating example implementation of a FIRfilter in an embodiment. The example implementation is described withrespect performance of a conventional FIR filter represented by:y[n]=Σ_(l=0) ^(L) b ₀[l]x[n−1], in that L is the order of theconventional FIR  (4)

In the embodiment, in block 610, coefficients b₀[l] of L order (L+1 tap)FIR filter are computed for a desired performance or filtercharacteristic.

In block 620, the difference coefficients b₁[l] representing differencebetween the adjacent coefficients (adjacent taps) are computed. Thedeference coefficients b₁[l] may be determined in an embodiment byrelation:b ₁[l]=b ₀[l]−b ₀[l−1] for every l=1 to L.  (5)

In block 630, an L−1 (order) or L tap difference FIR filter isimplemented using the coefficients b₁[l]. In one embodiment the L tapdifference FIR filter may be implemented using relation:

$\begin{matrix}{{y_{1}\lbrack n\rbrack} = {\sum\limits_{q = 0}^{L - 1}\;{\left( {b_{1}\lbrack q\rbrack} \right){X\left\lbrack {n - q - 1} \right\rbrack}}}} & (6)\end{matrix}$

In block 640, a compensation factor is computed. In one embodiment thecompensation factor is determined using relation:CF[n]=b ₀[0]x[n]+b ₀[L]x[n−(L+1)]+y[n−1]  (7)

In block 650, the filter output is generated by adding the L tapdifference FIR filter output y₁[n] to the compensation factor. In oneembodiment the filter output y[n] is generated by relationy[n]=y₁[n]+CF[n]. The filter operation in the embodiment may be may berepresented as:

$\begin{matrix}{{y\lbrack n\rbrack} = {{y\left\lbrack {n - 1} \right\rbrack} + {{b_{0}\lbrack 0\rbrack}{x\lbrack n\rbrack}} + {{b_{0}\lbrack L\rbrack}{x\left\lbrack {n - \left( {L + 1} \right)} \right\rbrack}} + {\sum\limits_{q = 0}^{L - 1}\;{\left( {b_{1}\lbrack q\rbrack} \right){x\left\lbrack {n - q - 1} \right\rbrack}}}}} & (8)\end{matrix}$

Due to computation of the difference, the coefficients b₁[l], may berepresented with fewer number of bits as against the b₀[l] therebyreducing the complexity of multiplication in terms of computationalpower or hardware requirement while maintaining the performance of thefilter on par with L order FIR filter with coefficients b₀[l] ofrelation (4). The relation (8) may be represented in frequency domain(for example, by taking Z-transform on both sides) as:

$\begin{matrix}{{Y\lbrack z\rbrack} = {\left\lbrack \frac{{z^{- 1}{B_{1}(z)}} + {b_{0}\lbrack 0\rbrack} - {{b_{0}\lbrack L\rbrack}z^{- {({L + 1})}}}}{1 - z^{- 1}} \right\rbrack{{X\lbrack z\rbrack}.}}} & \left( {8.a} \right)\end{matrix}$

FIG. 7 is a graph illustrating the values of b₀[l] and b₁[l] in anembodiment. In that, X axis representing number of taps in the filterand Y axis representing the values of the coefficients. The curve 710represents the smooth variation in the values of coefficients b₀[l] of aconventional FIR filter providing the desired performance. The curve 720represents the values of the coefficients b₁[l] computed as differencebetween the two adjacent coefficients of b₀[l] in one embodiment. As maybe observed, the magnitude of coefficients b₀[l] is smooth with peakvalue being greater than six hundred, thus requiring at least 10 bits torepresents each coefficient b₀[l]. On the other hand, the coefficientsb₁[l], do not exceed a value greater than thirty-two, thus requiring amaximum of 5 bits to represents the difference coefficients b₁[l].

FIG. 8A is an example FIR filter in one embodiment. The filter is showncomprising delay elements 810A through 810N, multiplier 830, first orderdifference filter 820, difference delay element 825, adder 840, andmultiplier 850, and feedback delay element 860. Each element isdescribed in further detail below.

The delay elements 810A through 810N generate sequence of samples thatare delayed by a factor. In one embodiment delay elements 810A through810N provides x[n−(L+1)] from x[n] there by providing an overall delayof [L+1] in accordance with the relation (8).

The first order difference filter 820 multiplies the input samples x[n]with the corresponding difference coefficients. In one embodiment, thefirst order difference filter 820 together with the difference delayelement 825 provides Σ_(q=0) ^(L−1)(b₁[q]) x[n−q−1] in the relation (8)by multiplying the input sample x[n] with corresponding coefficientvalue b₁[q]. In that, the bold lettered b₁[q] represents vector ofb₁[0], b₁[1], b₁[2], . . . b₁[L−1].

The multiplier 830 multiply delayed input samples with the coefficientto generate a component of the compensation factor. In one embodiment,the multiplier 830 multiply delayed sample x[n−(L+1)] with compensationfactor b₀[L] and provides the component b₀[L]x[n−(L+1)] in relation (7).

Similarly, the multiplier 850 provides the component in the compensationfactor. In one embodiment the multiplier 850 provides b₀[0]x[n] in therelation (7). The feedback delay element 860 provides the delayed outputsequence. In one embodiment, the feedback delay element 860 providesy[n−1] in relation (8).

The adder 840 adds the components provided by the elements 810, 830, 850and 860 to form filter output. In one embodiment, the adder adds thecomponents Σ_(q=0) ^(L−1)(b₁[q]) x[n−q−1], y[n−1], b₀[L]x[n−(L+1)] andb₀[0]x[n] to form the filter output y[n] in accordance with the relation(8).

FIG. 8B is an example filter in one embodiment. The filter 801 is showncomprising difference FIR filter 870, delay element 875, adder 880,feedback delay element 890, and compensation factor generator 895. Thedifference FIR filter 870 together with delay element 875 provide a L−1order FIR filter response with coefficients b₁[l] in accordance with therelation (6). The compensation factor generator 895 generate a value(factor) from the one or more coefficients b₀[l] and the input sequencex[n]. In one embodiment the factor is generated using relation:Compensation Factor=b ₀[0]x[n]+b ₀[L]x[n−(L+1)]  (9)

The feedback delay element 830 provides y[n−1] delayed (by unit time)output of the filter 801. The adder 880 performs summation operation andgenerates the filter output in accordance with the relation (8) forexample, adds the output of the difference FIR filter 810, output ofdelay element 830, and output of the factor generator 840 to provide thefilter output in an embodiment.

FIG. 9A is an example outputs of a conventional 200 tap low pass FIRfilter using b₀[l] coefficients quantized to 11 bits. FIG. 9B is anexample output of filter implemented as per the invention using b₁[l]coefficients represented by 6 bits. It may be observed that, the filteroutput of low pass difference FIR filter matches to that of conventionalFIR filter with a match greater than 60 dB. The manner in which theautoregressive filter as per the relation (2) may be implemented in anembodiment is further described below.

FIG. 10 is a block diagram illustrating example implementation of an IIRfilter in an embodiment. The example implementation is described withrespect performance of a conventional IIR filter represented by:y[n]=s[n]−Σ_(k=1) ^(K) a[k]y[n−k], in that K is the order of theconventional IIR.  (10)

In the embodiment, in block 1010, coefficients a[k] of K order IIRfilter are computed for a desired performance or filter characteristic.

In block 1020, the difference coefficients a₁[q] representing differencebetween the adjacent coefficients (adjacent taps) are computed. Thedeference coefficients a₁[q] may be determined in an embodiment byrelation:a ₁[q]=a[q+2]−a[q+1] for every q=0 to K−2.  (11)

In block 1030, a difference IIR filter is implemented using thecoefficients a₁[q]. In one embodiment the difference IIR filter may beimplemented using relation;

$\begin{matrix}{{y_{1}\lbrack n\rbrack} = {\sum\limits_{q = 0}^{K - 2}\;{\left( {a_{1}\lbrack q\rbrack} \right){y\left\lbrack {n - 2 - q} \right\rbrack}}}} & (12)\end{matrix}$

In block 1040, a compensation factor is computed. In one embodiment thecompensation factor is determined using relation:CF[n]=x[n]−x[n−1]−a[1]y[n−1]+a[K]y[n−(K+1)]+y[n−1]  (13)

In block 1050, the filter output is generated by subtracting thedifference IIR filter output y₁[n] from the compensation factor. In oneembodiment the filter output y[n] is generated by relationy[n]=CF[n]−y₁[n]. The filter operation in the embodiment may be may berepresented as:

$\begin{matrix}{{y\lbrack n\rbrack} = {\left( {{x\lbrack n\rbrack} - {x\left\lbrack {n - 1} \right\rbrack}} \right) - {{a\lbrack 1\rbrack}{y\left\lbrack {n - 1} \right\rbrack}} + {{a\lbrack K\rbrack}{y\left\lbrack {n - \left( {K + 1} \right)} \right\rbrack}} + {y\left\lbrack {n - 1} \right\rbrack} - {\sum\limits_{q = 0}^{K - 2}\;{\left( {a_{1}\lbrack q\rbrack} \right){y\left\lbrack {n - 2 - q} \right\rbrack}}}}} & (14)\end{matrix}$

Due to computation of the difference, the coefficients a₁[k], may berepresented with fewer number of bits as against the a[k] therebyreducing the complexity of multiplication in terms of computationalpower or hardware requirement while maintaining the performance of thefilter on par with Conventional IIR filter with coefficients a[k] ofrelation (10). The relation (14) may be represented in frequency domain(for example, by taking Z-transform on both sides) as:

$\begin{matrix}{{{Y\lbrack z\rbrack} = {\left\lbrack \frac{1 - z^{- 1}}{{1 - {z^{- 1}\left( {1 - {a\lbrack 1\rbrack}} \right)}} = {{z^{- 2}{{\overset{\_}{A}}_{1}(z)}} - {z^{- {({K + 1})}}{a\lbrack K\rbrack}}}} \right\rbrack{X\lbrack z\rbrack}}},} & \left( {14.a} \right)\end{matrix}$in that, Ā₁ represents the filter coefficients without a₀.

Similarly, the conventional ARMA filter 501 may be implemented withreduced hardware and processing complexity. In one embodiment, the FIRpart and IIR part of the conventional ARMA filter may be implemented byrelation 8 and 14 respectively to reduce the computational complexity.In one embodiment, the Filter implementation may be represented as:

$\begin{matrix}{{y\lbrack n\rbrack} = {{{b_{0}\lbrack 0\rbrack}{x\lbrack n\rbrack}} - {{b_{0}\lbrack L\rbrack}{x\left\lbrack {n - \left( {L + 1} \right)} \right\rbrack}} + {\sum\limits_{q = 0}^{L - 1}\;{\left( {b_{1}\lbrack q\rbrack} \right){x\left\lbrack {n - q - 1} \right\rbrack}}} + \left\lbrack {{{a\lbrack K\rbrack}{y\left\lbrack {n - \left( {K + 1} \right)} \right\rbrack}} + {\left( {1 - {a\lbrack 1\rbrack}} \right){y\left\lbrack {n - 1} \right\rbrack}} - {\sum\limits_{q = 0}^{K - 2}\;{\left( {a_{1}\lbrack q\rbrack} \right){y\left\lbrack {n - 2 - q} \right\rbrack}}}} \right.}} & (15)\end{matrix}$

Thus, one can see that the conventional ARMA filter can be implementedusing the individual difference filter for the MA and AR portion (510and 520) which results in bit-width savings of the multiplier and adderand hence complexity. The relation (15) may be represented in frequencydomain (for example, by taking Z-transform on both sides) as:

$\begin{matrix}{{Y\lbrack z\rbrack} = {\left\lbrack \frac{{z^{- 1}{B_{1}(z)}} + {b_{0}\lbrack 0\rbrack} - {{b_{0}\lbrack L\rbrack}z^{- {({L + 1})}}}}{1 - {{a\lbrack K\rbrack}z^{- {({K + 1})}}} - {z^{- 1}\left( {1 - {a\lbrack 1\rbrack}} \right)} + {z^{- 2}{{\overset{\_}{A}}_{1}(z)}}} \right\rbrack{X\lbrack z\rbrack}}} & \left( {15.a} \right)\end{matrix}$

In one embodiment, the precision of the accumulator (1−z⁻¹) is enhancedto maintain the stability of the filter. The manner in which thedifference FIR filter may be recursively deployed is described infurther detail below.

FIG. 11A through 11C are block diagrams illustrating recursivedeployment of the difference filters in one embodiment. FIG. 11A is anexample conventional N tap FIR filter 1101 with coefficients b₀[l]. FIG.11B is an example filter 1102 implemented with difference filter toprovide performance identical to the filter 1101 in an embodiment. Inthat, the filter 1102 is shown comprising first level difference FIRfilter 1110, delay element 1120, the first level adder 1130 and thefirst level delay element 1140. The first level adder 1130 receivescompensation factor CF as in relation (6) on path 1131. The elements,1110, 1120, 1130 and 1140 respectively operate similar to elements 870,875, 880, and 890 in the filter 801.

The FIG. 11C is an example filter 1103 implemented to providedperformance identical to filter 1101. In that, the first leveldifference FIR filter 1110 is implemented using a second leveldifference FIR filter 1150, delay element 1160, second level adder 1170and second level delay element 1180. The second level adder receives asecond compensation factor on path 1171 and may be represented as:Second Compensation Factor=b ₁[0]X[n]+b ₁[L−1]X[n−L]  (7)

The second level adder output is provided to the first level adder 1130.

The second level difference FIR filter 1150 is implemented usingcoefficients b₂[k]. The coefficients b₂[k] are derived as differencebetween the adjacent coefficients b₁[k]. Thus, the coefficients b₂[k]may be represents with lesser number of bits compared to thecoefficients b₁[k], thereby, further reducing the complexity.

The second level difference FIR filter 1150 is of N−2 taps while thefirst level difference FIR filter is of N−1 taps. As a result, thenumber of taps remains same at each level of recursion. Thus, thelatency is maintained as in the N tap FIR filter.

The use of difference FIR filter for implementing a FIR filter ofdesired performance, the number of bits required to store coefficientsis reduced at each level. Further the use of difference FIR filter forimplementing a FIR filter of desired performance maintain symmetry andanti-symmetry at all level thus ensuring the linear phase. Further, thedifference FIR filter may be deployed along with or on top of otherconventional complexity reduction techniques such as CSD representationfor example, for further reduction. The difference FIR filter may beimplemented for fixed coefficients and the programmable coefficients.

While various embodiments of the present disclosure have been describedabove, it should be understood that they have been presented by way ofexample only, and not limitation. Thus, the breadth and scope of thepresent disclosure should not be limited by any of the above-discussedembodiments, but should be defined only in accordance with the followingclaims and their equivalents.

What is claimed is:
 1. A method of filtering a digital signal with afirst filter performance comprising: determining a first set ofcoefficients that provide the first filter performance; computing asecond set of coefficients from the first set of coefficients; providingthe digital signal to a difference filter with second set ofcoefficients to produce a difference filter output; and adding acompensation factor to the difference filter output to generate afiltered output of the digital signal with a second filter performanceidentical to the first filter performance.
 2. The method of claim 1,wherein second set of coefficients are formed as difference between thesuccessive first set of coefficients such that when the first set ofcoefficients comprises N number of coefficients, the second set ofcoefficients comprises N−1 number of coefficients.
 3. The method ofclaim 1, wherein second set of coefficients are formed as differencebetween the non successive first set of coefficients such that when thefirst set of coefficients comprises N number of coefficients, the secondset of coefficients comprises N−1 number of coefficients.
 4. The methodof claim 1, further comprising: computing first set of coefficientsaccording to a first relation; computing the second set of coefficientsaccording to a second relation; generating the difference filter outputin accordance with a third relation; computing a compensation factor inaccordance with a fourth relation; and generating a filtered outputsamples from a set of input samples in accordance with a fifth relation.5. The method of claim 4, wherein: the first relation is y[n]=E_(l=0)^(L)b₀[l]x[n−1], in that the b₀ [l] representing first set ofcoefficients, y[n] is the digital filter output with first filterperformance, and x[n−l] representing the delayed input samples; thesecond relation is; b₁[l]=b₀[l]−b₀[l−1] for every l=1 to L, in that theb₁[l] representing the second set of coefficients, b₀ [l] and b₀ [l−1]representing the successive first set of coefficients; the thirdrelation is; y₁[n]=Σ_(q=0) ^(L−1)(b₁[q]) X[n−q−1], in that y1[n]representing the difference filter output; the fourth relation isCF[n]=b₀[0]x[n]+b₀ [L]x[n−(L+1)]+y[n−1] in that CF[n] representing thecompensation parameter; and the fifth relation isy˜[n]=y[n−1]+b ₀[0]x[n]+b ₀[L]x[n−(L+1)]+Σ_(q=0) ^(L−1)(b ₁[q])x[n−q−1], in that the y˜[n] representing the filtered output with secondperformance and x[n] representing the input samples.
 6. The method ofclaim 4, wherein, the first relation is y[n]=x[n]−Σ_(k=1) ^(K)a[k]y[n−k] in that the a[k] representing first set of coefficients, y[n]is the digital filter output with first filter performance, and x[n]representing the input samples; the second relation isa₁[q]=a[q+2]−a[q+1] for every q=0 to K−2, in that the a₁[q] representingthe second set of coefficients, a₀[q+2] and a₀[q+1] representing thesuccessive first set of coefficients; the third relation isy₁[n]=Σ_(q=0) ^(K−2)(a₁[q]) y[n−2−q], in that in that y1[n] representingthe difference filter output; the fourth relation isCF[n]=x[n]−x[n−1]−a[l]y[n−1]+a[K]y[n−(K+1)]+y[n−1] in that CF[n]representing the compensation parameter; and a filtered output withsecond performance follows the relationy˜[n]=(x[n]−x[n−1])−a[l]y[n−1]+a[K]y[n−(K+1)]+y[n−1]−Σ_(q=0) ^(K−2)(a₁[q]) y[n−2−q], in that the y˜[n] representing the filtered output withsecond performance and x[n] representing the input samples.
 7. Themethod of claim 1, further comprising; determining a third set ofcoefficients from the second set of coefficient; computing a secondlevel compensation factor from the first and the second set ofcoefficients; forming a second level difference digital filter withthird set of coefficients to produce a second level difference filteroutput; and adding the second level compensation factor to the secondlevel difference filter output to achieve a third performance identicalto the first filter performance, wherein the first set of coefficientscomprises N number of coefficients, the second set of coefficientscomprises N−1 number of coefficients and the third set of coefficientscomprises N−2 number of coefficients.
 8. A signal conditioning devicefor filtering a digital signal to provide a filtered output with a firstfiltering performance requiring a first set of coefficients ranging overfirst range value comprising: a first difference filter operative toprovide a first difference filter output wherein, the first differencefilter incorporating a second set of filter coefficients derived fromthe first set of filter coefficients wherein the second set of filtercoefficients ranging over a second range value lesser than the firstrange value; a first compensation factor generator operative to generatea first compensation factor; and an adder operative to add the firstdifference filter output, the first compensation factor, and thefiltered output delayed by a unit time to provide the filtered outputwithout using the first set of filter coefficients.
 9. The signalconditioning device of claim 8, wherein the first difference filtercomprising L numbers of taps and the difference filter implemented toaccording to a relation y₁[n]=Σ_(q=0) ^(L−1)(b₁[q]) X[n−q−1], in thaty₁[n] representing the first difference filter output, b₁[q]representing a first set of L tap coefficients, X[n−q−1] representingthe digital signal delayed by the corresponding q−1 unit time and theoperation within the summation indicating the multiplication operation.10. The signal conditioning device of claim 8, wherein the firstdifference filter comprising K−1 numbers of taps and the differencefilter implemented to according to a relation y₁[n]=Σ_(q=0)^(K−2)(a₁[q]) y[n−2−q], in that y₁[n] representing the first differencefilter output, a₁[q] representing a first set of K−1 tap coefficients,y[n−2−q] representing the filtered output signal delayed bycorresponding n−2−q unit time and operation within the summationindicating the multiplication operation.
 11. The signal conditioningdevice of claim 9, wherein the a first compensation factor is equal tob₀[0]x[n]+b₀[L]x[n−(L+1)], in that x[n] representing the digital signal,x[n−(L+1)] representing digital signal delayed by corresponding L+1 unittime, b₀[L] and b₀[0] respectively representing first constant and asecond constant providing a first filter performance.
 12. The signalconditioning device of claim 10, wherein the a first compensation factoris equal to x[n]−x[n−1]−a[l]y[n−1]+a[K]y[n−(K+1)]+y[n−1], in that x[n]representing the digital signal, x[n] and x[n−1)] representing thedigital signal and the digital signal delayed by unit time, y[n−(K+1)]and y[n−1] representing the filtered output delayed by K+1 units timeand one unit time, and a[l] and a[K] respectively representing a firstconstant and a second constant providing a first filter performance. 13.A signal conditioning device of claim 8, further comprising a seconddifference filter to provide a second difference filter output and asecond compensation factor generator to generate a second compensationfactor, wherein the adder is operative to add the first differencefilter output, second difference filter output, the first compensationfactor, the second compensation factor.
 14. The signal conditioningdevice of claim 13, wherein the first difference filter comprising Lnumbers of taps and the difference filter implemented to according to arelation y₁[n]=Σ_(q=0) ^(L−1)(b₁[q]) X[n−q−1], in that y₁[n]representing the first difference filter output, b₁[q] representing afirst set of L tap coefficients, X[n−q−1] representing the digitalsignal delayed by the corresponding q−1 unit time, and the seconddifference filter comprising K−1 numbers of taps and the seconddifference filter implemented according to a relation y₁[n]=Σ_(q=0)^(K−2)(a₁[q]) y[n−2−q], in that y₁[n] representing the second differencefilter output, a₁[q] representing a second set of K−1 tap coefficients,y[n−2−q] representing the filtered output signal delayed bycorresponding n−2−q unit time and the operation within the summationindicating the multiplication operation.
 15. A method of implementing adigital filter with a performance of an N tap Finite Impulse Response(FIR) filter comprising: determining a set of first coefficientscorresponding to an N taps of the FIR filter, wherein each of the firstcoefficient is represented with first number of bits; finding thedifference between the successive first coefficients of the N taps toform N−1 difference coefficients, wherein each of the N−1 differencecoefficients is represented with the second number of bits that is lessthan the first number of bits; Implementing N−1 taps FIR filter with N−1difference coefficients to provide difference filter output; adding afirst compensation factor to the difference filter output.
 16. Themethod of claim 15, further comprising: finding the difference betweenthe successive N−1 difference coefficients of to form N−2 differencecoefficients, wherein each the N−2 difference coefficients isrepresented with a third number of bits that is less than the secondnumber of bits; Implementing N−2 taps FIR filter with N−2 differencecoefficients to provide the difference filter output; adding a secondcompensation factor to the difference filter output.